I could somewhat see him trying to be fair after first acting out of spite. But why isn't the PBS NewsHour account labeled as government-funded media?

They are working on it. This is a new system a each label requires human research and consideration. They can’t do them all overnight.

Why start by labelling those entities you don't like, then changing the rules to allow for this label, and then slowly adding (or not) to other entities? It would be so easy to do it in a way that doesn't seem childish.